[R] Integration of functions with a vector argument

[Levine, Michael]

Dear Ivan,

Thank you very much for your suggestions. I understand what you are saying. I am afraid I didn't explain well enough what was needed, however.  Let us again restrict ourselves to the case of two dimensions. Then, what I have is a bivariate density function f(x,y) and my intention is to obtain f(x) by integrating out y. However, I don't only need to know the value of the marginal density f(x) at one point - I need to integrate it again to obtain the marginal cumulative density function F(x) as a next step. Thus, I also need to pass x as an additional parameter before integration, and this is what makes the problem more difficult.

I tried to do the following (here H and j are additional arguments needed to obtain the estimated bivariate density function):

f.int1 <- function(x,y) {Vectorize (function(y) f(c(x,y),H=H,j=j))}
    mrg.d1 <- function(x){
    integrate(f.int1,lower=-3,upper=3)$value
    }
mrg.cdf1 <- function(x){
    integrate(mrg.d1,lower=-Inf,upper=x)$value
    }

I received the following error message:


Error in integrate(f.int1, lower = -3, upper = 3) :
  evaluation of function gave a result of wrong length


How would you go about performing this task?

Yours sincerely,
Michael

Michael Levine
Associate Professor, Statistics

Department of Statistics
Purdue University
250 North University Street
West Lafayette, IN 47907 USA

email: mlevins using purdue.edu
Phone: +1-765-496-7571
Fax:   +1-765-494-0558
URL:   www.stat.purdue.edu/~mlevins
________________________________
From: Ivan Krylov <ikrylov using disroot.org>
Sent: Wednesday, June 12, 2024 6:41 AM
To: Levine, Michael <mlevins using purdue.edu>
Cc: r-help using r-project.org <r-help using r-project.org>
Subject: Re: [R] Integration of functions with a vector argument

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� Tue, 11 Jun 2024 18:44:08 +0000
"Levine, Michael" <mlevins using purdue.edu> �����:

> Let us say we have a function
>
> F <- function(x){ body of the function}
>
> Where x is, in general, a d by 1 vector with d>1.  Now I want to
> integrate out some of the coordinates of x, e.g. x[1] or x[2] or both
> of them etc. I'm well aware of how to integrate out e.g. y if a
> function is defined as f <- function (x,y) {body of the function}
> where y is a scalar.

The reason integrate() wants a separate function argument for the
integration coordinate is so that it could give the function a vector
of different values of the variable and receive a vector of the same
length containing the corresponding values of the function.

If the problem is small enough to make performance considerations
irrelevant, you can use Vectorize to make a function compatible with
integrate() from your function F:

x <- x0
z <- z0
Fiy <- Vectorize(function(y) F(c(x, y, z)))
integrate(Fiy, ymin, ymax)

The resulting function Fiy will accept a vector of values for y and
translate it into multiple calls to F with a three-element vector
argument as it expects.

Achieving better performance will require rewriting the function F to
be "vectorised", i.e. to accept vectors for arguments and return a
vector of the same length.

--
Best regards,
Ivan

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